Solving Problems Using Newton’s Laws: Ropes and Tension
- Tension is a stretching or straining force, for example, the force applied to a rope.
- An ideal rope doesn’t stretch, can only pull, and is massless.
- If a rope is massless, the net force on it is zero. The force on one end of the rope is equal in magnitude and opposite indirection to the force on the other end of the rope.
- Pulleys change the direction, but not the magnitude, of forces on ropes.
The diagram shows two carts attached by a string threaded through a frictionless pulley. Which of the following is the equation for the acceleration of the carts?
a = M2/(M1 + M2) (g)
The attached diagram shows two fingers pulling on opposite ends of a rope.
The force of the rope on one finger is equal in magnitude and opposite in direction to the force of the rope on the other finger. Which of the following equations correctly measures the result?
Fnet = F + (−F)
Which of the following does not describe a quality of the ideal rope as an instrument of force?
It has a consistent width.
The attached diagram shows two weights attached by a string going around a pulley.
The force of gravity is shown in the diagram as W. Assume there is no friction and an ideal rope is used. Weight M1 is very heavy and weight M2 is very light. Which of the following correctly describes what will happen in this system?
Because a net force (W) is being applied to the system, M2 will accelerate downward and, because of the tension in the rope, M1 will accelerate to the right at the same time
The attached force diagram shows a weight hanging by a rope.
The object is moving upward with a constant velocity. T equals the tension in the rope. The arrow indicates the positive component of the vector. Which of the following equations related to this experiment is not correct?
T + mg = Fnet
The diagram shows two carts attached by a rope going through a frictionless pulley. With respect to the diagram, which of the following is not correct?
T = −M 2g
The diagram shows two carts attached by a string that is threaded through a frictionless pulley. A net force, W, is being applied to the system. Which of the following equations for determining the value of T is correct?
T − M 2g = −M 2a
The diagram shows two carts attached by a string that is threaded through a frictionless pulley. A net force, W, is being applied to the system. Which of the following equations for determining the value of T is correct?
T = M 1a
Consider a rope with a mass hanging from it. The upward force holding this mass up is provided by the rope’s __________________.
tension
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1.1.1 Welcome to Physics5
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1.2.1 Physical Quantities and Units of Measurement14
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1.2.2 Unit Conversion and Dimensional Analysis11
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1.2.3 Uncertainty in Measurement and Significant Digits11
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1.3.1 The Basics of Vectors12
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1.3.2 Vector Components and Unit Vectors8
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1.4.1 The Scalar Product11
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1.5.1 The Vector Product3
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Unit 1 Practice Test18
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Unit 1 Test20
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2.1.1 Describing Motion11
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2.1.2 Displacement and Average Velocity11
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2.1.3 Understanding Instantaneous Velocity11
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2.1.4 Instantaneous Velocity and the Derivative11
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2.1.5 Acceleration10
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2.1.6 Another Look at Position, Velocity, and Acceleration11
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2.2.1 Describing Motion Under Constant Acceleration9
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2.2.2 Solving Problems Involving Motion Under Constant Acceleration10
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2.2.3 Free-Falling Objects11
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2.3.1 The Position and Velocity Vectors11
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2.3.2 The Acceleration Vector11
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2.3.3 Relating Position, Velocity, and Acceleration Vectors in Two Dimensions2
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2.4.1 A First Look at Projectile Motion11
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2.4.2 Understanding Projectile Motion10
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2.5.1 Describing Uniform Circular Motion9
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2.6.1 Understanding Relative Motion8
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Unit 2 Practice Test25
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Unit 2 Test25
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3.1.1 Newton's First Law10
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3.1.3 Introduction to Newton's Second Law10
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3.1.4 The Vector Nature of Force and Newton's Second Law10
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3.1.5 Weight9
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3.1.6 Actions, Reactions, and Newton's Third Law9
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3.2.1 Free-Body Diagrams10
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3.2.2 Solving Problems Using Newton's Laws: Ropes and Tension10
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3.2.3 Solving Problems Using Newton's Laws: Inclines and the Normal Force10
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3.3.1 Understanding the Frictional Force Between Two Surfaces8
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3.3.2 Problems on Friction and Inclines9
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3.3.3 Motion Through a Fluid: Drag Force and Terminal Speed10
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3.4.1 Forces and Uniform Circular Motion10
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3.4.2 Solving Circular Motion Problems9
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Unit 3 Practice Test25
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Unit 3 Test25
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4.1.1 The Work Done by a Constant Force in One Dimension9
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4.1.2 The Work Done by a Constant Force in Two Dimensions10
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4.1.3 The Work Done by a Variable Force10
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4.1.4 The Work Done by a Spring10
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4.2.1 The Work-Kinetic Energy Theorem8
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4.2.2 Solving Problems Involving Work and Kinetic Energy6
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4.2.3 Power10
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4.3.1 Work and Gravitational Potential Energy9
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4.3.2 Conservative and Nonconservative Forces10
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4.3.3 Calculating Potential Energy8
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4.4.1 Understanding Conservation of Mechanical Energy10
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4.4.3 Solving Problems Using Conservation of Mechanical Energy9
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4.4.4 Potential Energy Functions and Energy Diagrams8
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4.4.5 Work and Nonconservative Forces10
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4.4.7 Conservation of Energy in General10
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Unit 4 Practice Test25
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Unit 4 Test25
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5.1.1 Linear Momentum and Impulse8
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5.1.2 Solving Problems Using Linear Momentum and Impulse9
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5.1.3 Conservation of Momentum9
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5.1.4 Solving Problems Using Conservation of Momentum10
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5.1.5 Rocket Propulsion10
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5.2.1 Elastic Collisions in One Dimension8
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5.2.2 Inelastic Collisions in One Dimension10
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5.2.3 Collisions in Two Dimensions10
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Unit 5 Practice Test25
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Unit 5 Test25
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6.1.1 The Center of Mass of a System of Particles10
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6.1.2 The Center of Mass of a Rigid Body9
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6.1.3 The Center of Mass and the Motion of a System of Particles10
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6.2.1 Angular Displacement, Velocity, and Acceleration10
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6.2.2 Rotation with Constant Angular Acceleration9
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6.2.3 Relating Angular and Linear Quantities4
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6.3.1 The Kinetic Energy of Rotation10
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6.3.2 Calculating the Rotational Inertia of Solid Bodies9
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6.4.1 Torque8
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6.4.2 Newton's Second Law for Rotational Motion10
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6.4.3 Solving Problems Using Newton's Second Law for Rotational Motion10
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6.4.4 Work and Power in Rotational Motion9
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6.5.1 Understanding Rolling Motion10
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6.5.2 Solving Problems Involving Rolling Motion10
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6.6.1 The Definition of Angular Momentum10
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6.6.2 Torque and Angular Momentum9
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6.7.1 Understanding Conservation of Angular Momentum10
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6.7.3 Solving Problems Using Conservation of Angular Momentum10
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6.8.1 Understanding Precession8
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6.9.1 The Conditions for Static Equilibrium8
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6.9.2 Understanding Stable Equilibrium and the Center of Gravity9
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6.9.3 Solving Static Equilibrium Problems9
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Unit 6 Practice Test25
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Unit 6 Test24
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7.1.1 Newton's Law of Gravitation10
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7.1.2 Gravity on Earth9
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7.1.3 Weightlessness8
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7.1.4 Gravitational Potential Energy9
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7.2.1 Understanding Circular Orbital Motion10
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7.2.2 Kepler's Three Laws10
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7.2.3 Energy in Orbital Motion10
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Unit 7 Practice Test25
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Unit 7 Test25
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8.1.1 Fluids, Density, and Pressure10
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8.1.3 How Pressure Varies with Depth10
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8.1.7 Pascal's Principle and Examples of Hydrostatics9
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8.1.8 Buoyancy and Archimedes' Principle10
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8.2.1 Fluids in Motion: Streamlines and Continuity9
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8.2.2 Bernoulli's Equation10
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8.2.4 Fluids in the Real World: Surface Tension, Turbulence, and Viscosity10
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Unit 8 Practice Test25
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Unit 8 Test25
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9.1.1 Einstein's Postulates9
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9.1.2 The Relativity of Simultaneity10
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9.1.3 Time Dilation10
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9.1.4 Length Contraction10
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9.2.1 The Lorentz Transformation Equations10
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9.2.2 Solving Problems Using the Lorentz Transformations10
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9.3.1 Relativistic Momentum10
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9.3.2 Relativistic Energy10
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9.3.3 A Clock Story1
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Unit 9 Practice Test25
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Unit 9 Test25
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10.1.1 A Mass on a Spring: Simple Harmonic Motion10
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10.1.2 The Equations Describing Simple Harmonic Motion11
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10.1.3 Energy in Simple Harmonic Motion10
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10.2.1 The Simple Pendulum10
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10.2.2 Physical Pendulums5
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10.3.1 Damped Simple Harmonic Motion10
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10.3.2 Driven Oscillators10
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Unit 10 Practice Test25
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Unit 10 Test25
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11.1.1 Introduction to Waves10
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11.1.2 A Wave on a Rope: Frequency and Wavelength9
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11.1.3 A Wave on a Rope: Wave Speed10
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11.1.4 A Wave on a Rope: Energy and Power9
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11.2.1 Reflection, Transmission, and Superposition10
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11.2.2 Interference10
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11.3.1 Standing Waves: Two Waves Traveling in Opposite Directions7
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11.3.2 Standing Waves on a String9
